How do I reparent an entire model (and accompanying objects) to another armature?
This does indeed sound scriptable. Here's some docks.
Python API on parenting: https://docs.blender.org/api/current/bpy.types.Object.html?highlight=parent#bpy.types.Object.parent
Parenting Inverse explained: https://docs.blender.org/manual/en/latest/scene_layout/object/editing/parent.html?highlight=inverse%20parenting
The process sounds simple enough, though I don't know for sure without seeing the direct file.